I worked on a buddies 383 last year that had a dead cylinder from a burnt valve, it idled rougher than it should have but it didn't shake violently.

Is it worse in gear, even if you bring the revs up to the same as idle in park? Sounds like a busted motor or tranny mount to me.

Now I need to pin those needles, got to feel that heat
Hear my motor screamin while I'm tearin up the street